(%) -98 -87 -76 -64 -53 -42 -31 -20 -9 -2 13 24 35 47 58 69 80     Source: Michael C. Jensen, "The Performance of Mutual Funds in the Period 1945-1964," Journal of Finance 23 (May 1968).     intercepts) for the firms in our sample center around zero. If the initial expectation for al- pha were zero, as many firms would be expected to have a positive as a negative alpha for some sample period. The CAPM states that the expected value of alpha is zero for all se- curities, whereas the index model representation of the CAPM holds that the realized value of alpha should average out to zero for a sample of historical observed returns. Just as important, the sample alphas should be unpredictable, that is, independent from one sample period to the next. Some interesting evidence on this property was first compiled by Michael Jensen,8 who examined the alphas realized by mutual funds over the period 1945 to 1964. Figure 10.3 shows the frequency distribution of these alphas, which do indeed seem to be distributed around zero. We will see in Chapter 12 (Figure 12.10) that more recent studies come to the same conclusion. There is yet another applicable variation on the intuition of the index model, the mar- ket model. Formally, the market model states that the return "surprise" of any security is proportional to the return surprise of the market, plus a firm-specific surprise:   ri E(ri) i [rM E(rM)] ei   This equation divides returns into firm-specific and systematic components somewhat differently from the index model. If the CAPM is valid, however, you can see that, sub- stituting for E(ri) from equation 10.8, the market model equation becomes identical to the index model. For this reason the terms "index model" and "market model" are used interchangeably.